2. x = 1-1/(1+t), x'
y = 1+1/t, y'
t = 1 时, 切点是 (1/2, 2, 1),
切线向量是 (x'(1), y'(1), z'(1)) = (1/4, -1, 2)
切线方程是 (x-1/2)/(1/4) = (y-2)/(-1) = (z-1)/2
即 (4x-2)/1 =(y-2)/(-1) = (z-1)/2
法平面方程是 (1/4)(x-1/2) -(y-2) +2(z-1) = 0
即 2x-8y+16z-1 = 0
3. F = x^2+y^2-z, F'
切点是 (1, 2, 5), 法向量是 (2, 4, -1)
切平面方程 2(x-1)+4(y-2)-(z-5) = 0,
即 2x+4y-z -5 = 0
法线方程 (x-1)/2 = (y-2)/4 = (z-5)/(-1)